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A Class of "Central Limit Theorems" For Convolution Products of Generalized Functions

1969
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Transactions of the American Mathematical Society
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Introduction and summary. From the naive viewpoint of a nonprobabilist, the remarkable fact about the central limit theorem is that (under suitable conditions) the average of a large number of random variables converges (in a suitable sense) to a limit which is independent of the things being averaged, but is completely determined by the averaging process itself. In the present paper, this situation is abstracted from its connection with probability. As we shall see, the restriction to positive

doi:10.2307/1995123
fatcat:tm4fmbk7encv7gc6k6oyrtcmh4